The Mathematical Institute, University of Oxford, Eprints Archive

On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions

Griffiths, I. M. and Bain, C. D. and Breward, C. J. W. and Colegate, D. M. and Howell, P. D. and Waters, S. L. (2011) On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions. Journal of Colloid and Interface Science . (Submitted)

[img]
Preview
PDF
392Kb

Abstract

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1261
Deposited By:Peter Hudston
Deposited On:26 May 2011 07:44
Last Modified:08 Oct 2012 13:45

Repository Staff Only: item control page